# Boolean Functions, `equivalent` truth table and gate level implementation.

A boolean function is an expression consisting for binary variables, binary operators and constants (1 or 0). The Boolean function can be used to represent a logical scenario. Sometimes the functions can be minimized to lowest possible number of variables. In this section we will discuss boolean function with an example. We will also derive a truth-table and an equivalent gate level implementation.

Boolean `function` example: F1 = (x + y)z’

Where F1 is a Boolean function of binary variables and binary operators. The binary variables and operators are specified below.

Binary variables = x, y and z

Binary operators = Parentheses, NOT, AND and OR

Solving or minimization of the functions are performed in a particular precedence shown below.

LTE - 4G Wireless Technology

Digital fundamentals.

Interview Questions.

Operator precedence for evaluating Boolean Expressions.

Parentheses (Highest) > NOT > AND > OR (Lowest)

Next, we will discuss the equivalent truth table for boolean function F1.

Representation of Boolean function in Truth Table. The truth table above lists all the variables in function as inputs (x, y and z) and the output of function as column F1.  In order to derive a gate level implementation we will need to analyze all possible combination of inputs and corresponding output.

Next, we will discuss the equivalent gate level implementation for Function F1.

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Verilog Tutorial.

LTE Tutorial.

Memory Tutorial.

The circuit is most optimized implementation of the `boolean function.` F1 = (x + y)z’ Some more examples of Boolean Functions.

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